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Writing Radicals in Rational Form. Section 10.2. DEFINITIONS. Base: The term/variable of which is being raised upon Exponent: The term/variable is raised by a term. AKA Power. EXPONENT. BASE. THE EXPONENT. NTH ROOT RULE. M is the power (exponent) N is the root A is the base. - PowerPoint PPT Presentation
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04/22/23 22:18 10.2 - Rational Exponents 1
WRITING RADICALS IN RATIONAL WRITING RADICALS IN RATIONAL FORMFORM
Section 10.2
04/22/23 22:18 10.2 - Rational Exponents 2
DEFINITIONSDEFINITIONS
Base: The term/variable of which is being raised upon
Exponent: The term/variable is raised by a term. AKA Power
ma BASEEXPONENT
04/22/23 22:18 10.2 - Rational Exponents 3
THE EXPONENTTHE EXPONENT
ma 322 2 2 2 3 2 2 2
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NTH ROOT RULENTH ROOT RULE
• M is the power (exponent)• N is the root• A is the base
/m
m n na a
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RULESRULES
Another way of writing is 251/2. is written in radical expression form.251/2 is written in rational exponent form.
Why is square root of 25 equals out of 25 raised to ½ power?
2525
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EXAMPLE 1EXAMPLE 1
Evaluate 43/2 in radical form and simplify.
/m
m n na a
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EXAMPLE 1EXAMPLE 1
Evaluate 43/2 in radical form and simplify.
/m
m n na a
33/24 4
3 34 2
8
04/22/23 22:18 10.2 - Rational Exponents 8
EXAMPLE 2EXAMPLE 2Evaluate 41/2 in radical form and
simplify.
2
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YOUR TURNYOUR TURNEvaluate (–27)2/3 in radical form and
simplify.
04/22/23 22:18 10.2 - Rational Exponents10
EXAMPLE 3EXAMPLE 3
Evaluate –274/3 in radical form and simplify.
/m
m n na a
43 27
Hint: Remember, the negative is OUTSIDE of the base
81
Use calculator to check
04/22/23 22:18 10.2 - Rational Exponents11
EXAMPLE 4EXAMPLE 4Evaluate in radical form and simplify.
35 4 1x
3/54 1x
04/22/23 22:18 10.2 - Rational Exponents 12
NTH ROOT RULENTH ROOT RULE
• M is the power (exponent)• N is the root• A is the base
DROP AND SWAP
//
1mm n n
m na aa
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EXAMPLE 5EXAMPLE 5Evaluate (27)–2/3 in radical form and simplify.
19
2/327 23 27
23
1
27
213
04/22/23 22:18 10.2 - Rational Exponents 14
EXAMPLE 6EXAMPLE 6Evaluate (–64)–2/3 in radical form and
simplify.
116
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YOUR TURNYOUR TURNEvaluate in radical form and simplify.
1 1
1 1
25 36
36 25
1/22536
65
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PROPERTIES OF EXPONENTSPROPERTIES OF EXPONENTS
Product of a Power:
Power of a Power:
Power of a Product:
Negative Power Property:
Quotient Power Property:
m n m na a a ( ) m n m na a
( ) m m mab a b( )
1nnaa
mm n
n
a aa
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EXAMPLEEXAMPLE 7 7Simplify
• Saying goes: BASE, BASE, ADD
If the BASES are the same, ADD the powersm n m na a a
4 52 2
92
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EXAMPLE 8EXAMPLE 8Simplify 1/2 1/3x x
5/6x
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YOUR TURNYOUR TURNSimplify 3/5 1/4x x
17/20x
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EXAMPLE 9EXAMPLE 9Simplify
• Saying goes: POWER, POWER, MULTIPLY
If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES
( ) m n m na a
542
202
04/22/23 22:18 10.2 - Rational Exponents 21
EXAMPLE 10EXAMPLE 10Simplify
( ) m m mab a b
52/52x
232x
/ ( / )( )52 5 5 2 5 52 2x x
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YOUR TURNYOUR TURNSimplify 41/4 2/33x y
2/3
81xy
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EXAMPLE 11EXAMPLE 11Simplify
• Saying goes: When dividing an expression with a power, SUBTRACT the powers.
m
m nn
a aa
1/3
4/3
77
17
// /
/
1 31 3 4 3
4 3
7 77
04/22/23 22:19 10.2 - Rational Exponents 24
EXAMPLE 12EXAMPLE 12Simplify
3
xx
1/6x
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EXAMPLE 13EXAMPLE 13Simplify
33 4
5
xx x
x
13/60x